I just checked it carefully again.
The current disappears at 1.4V. It starts to decrease when the control signal is at 1.45V and within several mV of difference, the current is completely gone. It seems the difference is the threshold voltage of the device (documented Vtlin=355mV+/-45mV).
I did the following:
at power up, current = 85mA
at control signal = 1.8V, current = 85mA
at control signal = 1.45V, current start to decrease
at control signal = 1.4V, current = 0
at control signal = back to 1.8V, current =85mA